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Binary Opinion Dynamics with Stubborn Agents

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TLDR
It is shown that the presence of stubborn agents with opposing opinions precludes convergence to consensus; instead, opinions converge in distribution with disagreement and fluctuations.
Abstract
We study binary opinion dynamics in a social network with stubborn agents who influence others but do not change their opinions. We focus on a generalization of the classical voter model by introducing nodes (stubborn agents) that have a fixed state. We show that the presence of stubborn agents with opposing opinions precludes convergence to consensus; instead, opinions converge in distribution with disagreement and fluctuations. In addition to the first moment of this distribution typically studied in the literature, we study the behavior of the second moment in terms of network properties and the opinions and locations of stubborn agents. We also study the problem of optimal placement of stubborn agents where the location of a fixed number of stubborn agents is chosen to have the maximum impact on the long-run expected opinions of agents.

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Citations
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Journal ArticleDOI

Opinion Dynamics on Networks under Correlated Disordered External Perturbations.

TL;DR: In this article, the authors study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks, and show analytically that the vote-share variability is directly related to the external influence fluctuations.
Posted Content

Blind Community Detection from Low-rank Excitations of a Graph Filter

TL;DR: In this paper, the authors proposed a spectral method to detect communities in a graph from the observation of signals at its nodes, where the observed signals are noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations.
Proceedings ArticleDOI

A novel homogenous protocol for multi-agent clustering over directed graphs

TL;DR: A novel homogenous distributed protocol that can provide both consensus and clustering of identical agents, interacting over general directed graph, and establish criteria for their convergence is offered.
Journal ArticleDOI

Bots influence opinion dynamics without direct human-bot interaction: the mediating role of recommender systems

TL;DR: In this article , a simple recommendation system mediates the agents' content consumption, thus influencing opinions without direct human-bot interaction, and the authors show that even with limited direct interactions, the mere presence of the bot is sufficient to shift the average population's opinion.
Journal ArticleDOI

Clustering and stubbornness regulate the formation of echo chambers in personalised opinion dynamics

TL;DR: In this article , a mechanistic model of opinions on clustered dynamic social networks with sorting algorithms was studied and it was shown that local social clustering is a key structure to form echo chambers and in combination with community structure can further increase polarisation, particularly with reinforcing algorithms.
References
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Journal ArticleDOI

A Simple Model of Herd Behavior

TL;DR: In this article, the authors analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision, and they show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior.
Proceedings ArticleDOI

Maximizing the spread of influence through a social network

TL;DR: An analysis framework based on submodular functions shows that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models, and suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.
Journal ArticleDOI

A New Product Growth for Model Consumer Durables

TL;DR: A growth model for the timing of initial purchase of new products is developed and tested empirically against data for eleven consumer durables, and a long-range forecast is developed for the sales of color television sets.
Journal ArticleDOI

Maximizing the Spread of Influence through a Social Network

TL;DR: The problem of finding the most influential nodes in a social network is NP-hard as mentioned in this paper, and the first provable approximation guarantees for efficient algorithms were provided by Domingos et al. using an analysis framework based on submodular functions.
Book

Interacting Particle Systems

TL;DR: The construction, and other general results are given in this paper, with values in [0, ] s. The voter model, the contact process, the nearest-particle system, and the exclusion process.
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